On the Optimal Blocking Factor for Blocked, Non-overlapped Multiprocessor Schedules

This paper addresses the issue of determining the blocked non-overlapped multiprocessor schedule of optimal blocking factor for signal processing programs expressed as synchronous dataflow (SDF) graphs. The main result of this paper is a graph-theoretic characterization of the behavior of the critical path in the precedence graph of blocking factor as is increased. We show that the asymptotic behavior is cyclic in the following sense: there exist constants and such that the critical path in the precedence graph of blocking factor has weight given by (EQ 1) where is the maximum cycle mean in the original graph, and is an integer computable from the graph. 1. Introduction Synchronous Dataflow (SDF) [2] is a subset of dataflow [6] that has proven to be an elegant model for expressing signal processing programs. In the SDF model, the program is represented as a graph where the nodes represent computations and the arcs represent communication channels and precedence constraints. Each acto..